Metrology by reconstruction

ABSTRACT

Disclosed herein is a method comprising: obtaining a plurality of measurement results from a pattern on a substrate respectively using a plurality of substrate measurement recipes, the substrate processed by a lithography process; reconstruct, using a computer, the pattern using the plurality of measurement results, to obtain a reconstructed pattern.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority of U.S. application 62/273,944 whichwas filed on Dec. 31, 2015 and which is incorporated herein in itsentirety by reference.

TECHNICAL FIELD

The description herein relates to lithographic apparatuses andprocesses, and more particularly to a tool and a method to inspect ormeasure substrates produced by the lithographic apparatuses andprocesses.

BACKGROUND

A lithographic apparatus can be used, for example, in the manufacture ofintegrated circuits (ICs) or other devices. In such a case, a patterningdevice (e.g., a mask) may contain or provide a circuit patterncorresponding to an individual layer of the device (“design layout”),and this circuit pattern can be transferred onto a target portion (e.g.comprising one or more dies) on a substrate (e.g., silicon wafer) thathas been coated with a layer of radiation-sensitive material (“resist”),by methods such as irradiating the target portion through the circuitpattern on the patterning device. In general, a single substratecontains a plurality of adjacent target portions to which the circuitpattern is transferred successively by the lithographic apparatus, onetarget portion at a time. In one type of lithographic apparatus, thecircuit pattern on the entire patterning device is transferred onto onetarget portion in one go; such an apparatus is commonly referred to as awafer stepper. In an alternative apparatus, commonly referred to as astep-and-scan apparatus, a projection beam scans over the patterningdevice in a given reference direction (the “scanning” direction) whilesynchronously moving the substrate parallel or anti-parallel to thisreference direction. Different portions of the circuit pattern on thepatterning device are transferred to one target portion progressively.

Prior to transferring the circuit pattern from the patterning device tothe substrate, the substrate may undergo various procedures, such aspriming, resist coating and a soft bake. After exposure, the substratemay be subjected to other procedures, such as a post-exposure bake(PEB), development, a hard bake and measurement/inspection of thetransferred circuit pattern. This array of procedures is used as a basisto make an individual layer of a device, e.g., an IC. The substrate maythen undergo various procedures such as etching, ion-implantation(doping), metallization, oxidation, chemo-mechanical polishing, etc.,all intended to finish off the individual layer of the device. Ifseveral layers are required in the device, then some or all of theseprocedures or a variant thereof may be repeated for each layer.Eventually, a device will be present in each target portion on thesubstrate. If there are a plurality of devices, these devices are thenseparated from one another by a technique such as dicing or sawing,whence the individual devices can be mounted on a carrier, connected topins, etc.

SUMMARY

Disclosed herein is a method comprising: obtaining a plurality ofmeasurement results from a pattern on a substrate respectively using aplurality of substrate measurement recipes, the substrate processed by alithography process; reconstruct, using a computer, the pattern usingthe plurality of measurement results, to obtain a reconstructed pattern.

According to an embodiment, reconstructing the pattern is by using theAlgebraic Reconstruction Technique, the Radon transform, or theprojection-slice theorem.

According to an embodiment, reconstructing the pattern does not use theentirety of each of the plurality of measurement results.

According to an embodiment, the plurality of measurement resultscomprise diffraction images.

According to an embodiment, at least two of the plurality of substratemeasurement recipes differ in intensity distribution at a pupil plane ofa metrology tool used in obtaining the measurement results.

According to an embodiment, at least two of the plurality of substratemeasurement recipes differ in a wavelength or a polarization of lightused in obtaining the measurement results.

According to an embodiment, the method further comprises determining anedge placement error or a dimension using the reconstructed pattern.

According to an embodiment, the method further comprises aligning apatterning device to the pattern using the reconstructed pattern.

According to an embodiment, the method further comprises determiningalignment between two sub-patterns of the pattern, wherein the twosub-patterns are on different layers of the substrate.

According to an embodiment, obtaining a plurality of measurement resultscomprises illuminating the pattern with ultraviolet light or X-ray.

According to an embodiment, the method further comprises determining atrue value of a measured characteristic of the pattern, using thereconstructed pattern.

According to an embodiment, the method further comprises determining asystematic error of a measured characteristic of the pattern, using thereconstructed pattern.

According to an embodiment, the pattern has an asymmetry.

According to an embodiment, the pattern has a tilted bottom.

According to an embodiment, the pattern has a tilted sidewall.

Disclosed herein is a computer program product comprising a computerreadable medium having instructions recorded thereon, the instructionswhen executed by a computer implementing any of the above methods.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of various subsystems of a lithography system.

FIG. 2A schematically depicts a method of predicting defects in alithographic process.

FIG. 2B is schematic diagram of a dark field measurement apparatus foruse in measuring targets according to embodiments of the invention usinga first pair of illumination apertures providing certain illuminationmodes.

FIG. 2C is a schematic detail of a diffraction spectrum of a target fora given direction of illumination.

FIG. 2D is a schematic illustration of a second pair of illuminationapertures providing further illumination modes in using a measurementapparatus for diffraction based overlay measurements.

FIG. 2E is a schematic illustration of a third pair of illuminationapertures combining the first and second pairs of apertures providingfurther illumination modes in using a measurement apparatus fordiffraction based overlay measurements.

FIG. 2F depicts a form of multiple periodic structure (e.g., multiplegrating) target and an outline of a measurement spot on a substrate.

FIG. 2G depicts an image of the target of FIG. 2F obtained in theapparatus of FIG. 2B.

FIG. 3 schematically shows a substrate with two distinct targets P andQ, where copies of each are placed in four different areas of thesubstrate.

FIG. 4A and FIG. 4B demonstrate how the same target may introducedifferent systematic errors in different substrate measurement recipes.

FIG. 5A shows two diffraction images obtained using substratemeasurement recipes with two different intensity distributions at thepupil plane of the metrology tool.

FIG. 5B shows the pattern from which the two diffraction images of FIG.5A are obtained.

FIG. 5C, FIG. 5D and FIG. 5E each show the average difference (verticalaxes) between the two diffraction images of FIG. 5A as a function ofposition (horizontal axes), respectively with zero to increasing amountsof asymmetry.

FIG. 6 schematically shows a flow for reconstruction.

FIGS. 7A-7D each show a different intensity distribution at the pupilplane, the image it leads to, and the portion of the image used by thereconstruction algorithm.

FIG. 8 schematically shows an example of reconstruction of a pattern.

FIGS. 9A-9C schematically show several uses of the reconstructedpattern.

FIG. 10 is a block diagram of an example computer system.

FIG. 11 is a schematic diagram of a lithographic apparatus.

FIG. 12 is a schematic diagram of another lithographic apparatus.

FIG. 13 is a more detailed view of the apparatus in FIG. 12.

DETAILED DESCRIPTION

Although specific reference may be made in this text to the manufactureof ICs, it should be explicitly understood that the description hereinhas many other possible applications. For example, it may be employed inthe manufacture of integrated optical systems, guidance and detectionpatterns for magnetic domain memories, liquid-crystal display panels,thin-film magnetic heads, etc. The skilled artisan will appreciate that,in the context of such alternative applications, any use of the terms“reticle”, “wafer” or “die” in this text should be considered asinterchangeable with the more general terms “mask”, “substrate” and“target portion”, respectively.

In the present document, the terms “radiation” and “beam” are used toencompass all types of electromagnetic radiation, including ultravioletradiation (e.g. with a wavelength of 365, 248, 193, 157 or 126 nm) andEUV (extreme ultra-violet radiation, e.g. having a wavelength in therange 5-20 nm).

The term “optimizing” and “optimization” as used herein mean adjustingan apparatus, e.g., a lithographic apparatus, such that devicefabrication results and/or processes (e.g., of lithography) have one ormore desirable characteristics, such as higher accuracy of projection ofa design layout on a substrate, larger process window, etc.

As a brief introduction, FIG. 1 illustrates an exemplary lithographicapparatus 10A. Major components include illumination optics which definethe partial coherence (denoted as sigma) and which may include optics14A, 16Aa and 16Ab that shape radiation from a radiation source 12A,which may be a deep-ultraviolet excimer laser source or other type ofsource including an extreme ultra violet (EUV) source (as discussedherein, the lithographic apparatus itself need not have the radiationsource); and optics 16Ac that project an image of a patterning devicepattern of a patterning device 18A onto a substrate plane 22A. Anadjustable filter or aperture 20A at the pupil plane of the projectionoptics may restrict the range of beam angles that impinge on thesubstrate plane 22A, where the largest possible angle defines thenumerical aperture of the projection optics NA=sin(Θ_(max)).

In a lithographic apparatus, projection optics direct and shape theillumination from a source via a patterning device and onto a substrate.The term “projection optics” is broadly defined here to include anyoptical component that may alter the wavefront of the radiation beam.For example, projection optics may include at least some of thecomponents 14A, 16Aa, 16Ab and 16Ac. An aerial image (AI) is theradiation intensity distribution at substrate level. A resist layer onthe substrate is exposed and the aerial image is transferred to theresist layer as a latent “resist image” (RI) therein. The resist image(RI) can be defined as a spatial distribution of solubility of theresist in the resist layer. A resist model can be used to calculate theresist image from the aerial image, an example of which can be found inU.S. Patent Application Publication No. US 2009-0157630, the disclosureof which is hereby incorporated by reference in its entirety. The resistmodel is related only to properties of the resist layer (e.g., effectsof chemical processes that occur during exposure, post-exposure bake(PEB) and development). Optical properties of the lithographic apparatus(e.g., properties of the source, the patterning device and theprojection optics) dictate the aerial image. Since the patterning deviceused in the lithographic apparatus can be changed, it is desirable toseparate the optical properties of the patterning device from theoptical properties of the rest of the lithographic apparatus includingat least the source and the projection optics.

As shown in FIG. 2A, the lithographic apparatus LA may form part of alithographic cell LC, also sometimes referred to as a lithocell orlithocluster, which also includes apparatus to perform one or more pre-and post-exposure processes on a substrate. Conventionally these includeone or more spin coaters SC to deposit a resist layer, one or moredevelopers DE to develop exposed resist, one or more chill plates CH andone or more bake plates BK. A substrate handler, or robot, RO picks up asubstrate from input/output ports I/O1, I/O2, moves it between thedifferent process devices and delivers it to the loading bay LB of thelithographic apparatus. These devices, which are often collectivelyreferred to as the track, are under the control of a track control unitTCU which is itself controlled by the supervisory control system SCS,which also controls the lithographic apparatus via lithographic controlunit LACU. Thus, the different apparatus may be operated to maximizethroughput and processing efficiency. The lithographic cell LC mayfurther comprises one or more etchers to etch the substrate and one ormore measuring devices configured to measure a parameter of thesubstrate. The measuring device may comprise an optical measurementdevice configured to measure a physical parameter of the substrate, suchas a scatterometer, a scanning electron microscope, etc.

In a semiconductor device fabrication process (e.g., lithographyprocess), a substrate may be subjected to various types of measurementduring or after the process. The measurement may determine whether aparticular substrate is defective, may establish adjustments to theprocess and apparatuses used in the process (e.g., aligning two layerson the substrate or aligning the mask to the substrate), may measure theperformance of the process and the apparatuses, or may be for otherpurposes. Examples of substrate measurement include optical imaging(e.g., optical microscope), non-imaging optical measurement (e.g.,measurement based on diffraction such as ASML YieldStar, ASML SMASHGridAlign), mechanical measurement (e.g., profiling using a stylus,atomic force microscopy (AFM)), non-optical imaging (e.g., scanningelectron microscopy (SEM)). The SMASH (SMart Alignment Sensor Hybrid)system, as described in U.S. Pat. No. 6,961,116, which is incorporate byreference herein in its entirety, employs a self-referencinginterferometer that produces two overlapping and relatively rotatedimages of an alignment marker, detects intensities in a pupil planewhere Fourier transforms of the images are caused to interfere, andextracts the positional information from the phase difference betweendiffraction orders of the two images which manifests as intensityvariations in the interfered orders.

The term “substrate measurement recipe” may include parameters of themeasurement itself, parameters of the patterns measured, or both. Forexample, if the measurement used in a substrate measurement recipe isnon-imaging diffraction-based optical measurement, the parameters of themeasurement may include the wavelength, the polarization, the incidentangle relative to the substrate, the relative orientation relative to apattern on the substrate, of the light diffracted. The parameters of themeasurement may include parameters of the metrology apparatus used inthe measurement. The patterns measured may be patterns whose diffractionis measured. The patterns measured may be patterns specially designedfor measurement purposes (also known as “targets” or “targetstructures”). Multiple copies of a target may be placed on many placeson a substrate. The parameters of the patterns measured may include theshape, orientation and size of these patterns. A substrate measurementrecipe may be used to align a layer of patterns being imaged againstexisting patterns on a substrate. A substrate measurement recipe may beused to align the patterning device to the substrate, by measuring therelative position of the substrate.

A substrate measurement recipe may be expressed in a mathematical form:(r₁, r₂, r₃, . . . r_(n); t₁, t₂, t₃, . . . t_(n)), where r_(i) areparameters of the measurement and t_(j) are parameters of the patternsmeasured. FIG. 3 schematically shows a substrate with two distincttargets P and Q, where copies of each are placed in four different areasof the substrate. The targets may include gratings, e.g., of mutuallyperpendicular directions. The target may include locations on a patternwhere a measurement can detect displacement of an edge of the pattern ora dimension of the pattern. The substrate of FIG. 3 may be subjected tomeasurement using two substrate measurement recipes A and B. Substratemeasurement recipes A and B at least differ on the target measured(e.g., A measures target P and B measures target Q). Substratemeasurement recipes A and B may also differ on the parameters of theirmeasurement. Substrate measurement recipes A and B may not even be basedon the same measurement technique. For example recipe A may be based onSEM measurement and recipe B may be based on AFM measurement.

A target used by a scatterometer may comprise a relatively largeperiodic structure layout (e.g., comprising one or more gratings), e.g.,40 μm by 40 μm. In that case, the measurement beam often has a spot sizethat is smaller than the periodic structure layout (i.e., the layout isunderfilled such that one or more of the periodic structures is notcompletely covered by the spot). This simplifies mathematicalreconstruction of the target as it can be regarded as infinite. However,for example, when the target can be positioned in among productfeatures, rather than in a scribe lane, the size of a target may bereduced, e.g., to 20 μm by 20 μm or less, or to 10 μm by 10 μm or less.In this situation, the periodic structure layout may be made smallerthan the measurement spot (i.e., the periodic structure layout isoverfilled). Typically such a target is measured using dark fieldscatterometry in which the zeroth order of diffraction (corresponding toa specular reflection) is blocked, and only higher orders processed.Examples of dark field metrology can be found in PCT patent applicationpublication nos. WO 2009/078708 and WO 2009/106279, which are herebyincorporated in their entirety by reference. Further developments of thetechnique have been described in U.S. patent application publicationsUS2011/0027704, US2011/0043791 and US2012/0242970, which are herebyincorporated in their entirety by reference. Diffraction-based overlayusing dark-field detection of the diffraction orders enables overlaymeasurements on smaller targets. These targets can be smaller than theillumination spot and may be surrounded by product structures on asubstrate. In an embodiment, multiple targets can be measured in oneimage.

In an embodiment, the target on a substrate may comprise one or more 1-Dperiodic gratings, which are printed such that after development, thebars are formed of solid resist lines. In an embodiment, the target maycomprise one or more 2-D periodic gratings, which are printed such thatafter development, the one or more gratings are formed of solid resistpillars or vias in the resist. The bars, pillars or vias mayalternatively be etched into the substrate. The pattern of the gratingis sensitive to chromatic aberrations in the lithographic projectionapparatus, particularly the projection system PL, and illuminationsymmetry and the presence of such aberrations will manifest themselvesin a variation in the printed grating. Accordingly, the measured data ofthe printed gratings can be used to reconstruct the gratings. Theparameters of the 1-D grating, such as line widths and shapes, orparameters of the 2-D grating, such as pillar or via widths or lengthsor shapes, may be input to the reconstruction process, performed byprocessing unit PU, from knowledge of the printing step and/or othermeasurement processes.

A dark field metrology apparatus is shown in FIG. 2B. A target T(comprising a periodic structure such as a grating) and diffracted raysare illustrated in more detail in FIG. 2C. The dark field metrologyapparatus may be a stand-alone device or incorporated in either thelithographic apparatus LA, e.g., at the measurement station, or thelithographic cell LC. An optical axis, which has several branchesthroughout the apparatus, is represented by a dotted line O. In thisapparatus, radiation emitted by an output 11 (e.g., a source such as alaser or a xenon lamp or an opening connected to a source) is directedonto substrate W via a prism 15 by an optical system comprising lenses12, 14 and objective lens 16. The radiation may be ultraviolet light orX-ray. These lenses are arranged in a double sequence of a 4Farrangement. A different lens arrangement can be used, provided that itstill provides a substrate image onto a detector.

The lens arrangement may allow for access of an intermediate pupil-planefor spatial-frequency filtering. Therefore, the angular range at whichthe radiation is incident on the substrate can be selected by defining aspatial intensity distribution in a plane that presents the spatialspectrum of the substrate plane, here referred to as a (conjugate) pupilplane. In particular, this can be done, for example, by inserting anaperture plate 13 of suitable form between lenses 12 and 14, in a planewhich is a back-projected image of the objective lens pupil plane. Inthe example illustrated, aperture plate 13 has different forms, labeled13N and 13S, allowing different illumination modes to be selected. Theillumination system in the present examples forms an off-axisillumination mode. In the first illumination mode, aperture plate 13Nprovides off-axis illumination from a direction designated, for the sakeof description only, as ‘north’. In a second illumination mode, apertureplate 13S is used to provide similar illumination, but from an oppositedirection, labeled ‘south’. Other modes of illumination are possible byusing different apertures. The rest of the pupil plane is desirably darkas any unnecessary radiation outside the desired illumination mode mayinterfere with the desired measurement signals. The parameters of themeasurement of a substrate measurement recipe may include the intensitydistribution at the pupil plane. A target may be measured using multiplesubstrate measurement recipes that differ in the intensity distributionat the pupil plane.

As shown in FIG. 2C, target T is placed with substrate W substantiallynormal to the optical axis O of objective lens 16. A ray of illuminationI impinging on target T from an angle off the axis O gives rise to azeroth order ray (solid line 0) and two first order rays (dot-chain line+1 and double dot-chain line −1). With an overfilled small target T,these rays are just one of many parallel rays covering the area of thesubstrate including metrology target T and other features. Since theaperture in plate 13 has a finite width (necessary to admit a usefulquantity of radiation), the incident rays I will in fact occupy a rangeof angles, and the diffracted rays 0 and +1/−1 will be spread outsomewhat. According to the point spread function of a small target, eachorder +1 and −1 will be further spread over a range of angles, not asingle ideal ray as shown. Note that the periodic structure pitch andillumination angle can be designed or adjusted so that the first orderrays entering the objective lens are closely aligned with the centraloptical axis. The rays illustrated in FIG. 2B and FIG. 2C are shownsomewhat off axis, purely to enable them to be more easily distinguishedin the diagram.

At least the 0 and +1 orders diffracted by the target on substrate W arecollected by objective lens 16 and directed back through prism 15.Returning to FIG. 2B, both the first and second illumination modes areillustrated, by designating diametrically opposite apertures labeled asnorth (N) and south (S). When the incident ray I is from the north sideof the optical axis, that is when the first illumination mode is appliedusing aperture plate 13N, the +1 diffracted rays, which are labeled+1(N), enter the objective lens 16. In contrast, when the secondillumination mode is applied using aperture plate 13S the −1 diffractedrays (labeled −1(S)) are the ones which enter the lens 16. Thus, in anembodiment, measurement results are obtained by measuring the targettwice under certain conditions, e.g., after rotating the target orchanging the illumination mode or changing the imaging mode to obtainseparately the −1^(st) and the +1^(st) diffraction order intensities.Comparing these intensities for a given target provides a measurement ofasymmetry in the target, and asymmetry in the target can be used as anindicator of a parameter of a lithography process, e.g., overlay error.In the situation described above, the illumination mode is changed.

A beam splitter 17 divides the diffracted beams into two measurementbranches. In a first measurement branch, optical system 18 forms adiffraction spectrum (pupil plane image) of the target on first sensor19 (e.g. a CCD or CMOS sensor) using the zeroth and first orderdiffractive beams. Each diffraction order hits a different point on thesensor, so that image processing can compare and contrast orders. Thepupil plane image captured by sensor 19 can be used for focusing themetrology apparatus and/or normalizing intensity measurements of thefirst order beam. The pupil plane image can also be used for manymeasurement purposes such as reconstruction, which are not described indetail here.

In the second measurement branch, optical system 20, 22 forms an imageof the target on the substrate W on sensor 23 (e.g. a CCD or CMOSsensor). In the second measurement branch, an aperture stop 21 isprovided in a plane that is conjugate to the pupil-plane. Aperture stop21 functions to block the zeroth order diffracted beam so that the imageDF of the target formed on sensor 23 is formed from the −1 or +1 firstorder beam. The images captured by sensors 19 and 23 are output to imageprocessor and controller PU, the function of which will depend on theparticular type of measurements being performed. Note that the term‘image’ is used here in a broad sense. An image of the periodicstructure features (e.g., grating lines) as such will not be formed, ifonly one of the −1 and +1 orders is present.

The particular forms of aperture plate 13 and stop 21 shown in FIG. 2Dand FIG. 2E are purely examples. In another embodiment of the invention,on-axis illumination of the targets is used and an aperture stop with anoff-axis aperture is used to pass substantially only one first order ofdiffracted radiation to the sensor. In yet other embodiments, 2nd, 3rdand higher order beams (not shown) can be used in measurements, insteadof or in addition to the first order beams.

In order to make the illumination adaptable to these different types ofmeasurement, the aperture plate 13 may comprise a number of aperturepatterns formed around a disc, which rotates to bring a desired patterninto place. Note that aperture plate 13N or 13S are used to measure aperiodic structure of a target oriented in one direction (X or Ydepending on the set-up). For measurement of an orthogonal periodicstructure, rotation of the target through 90° and 270° might beimplemented. Different aperture plates are shown in FIG. 2D and FIG. 2E.FIG. 2D illustrates two further types of off-axis illumination mode. Ina first illumination mode of FIG. 2D, aperture plate 13E providesoff-axis illumination from a direction designated, for the sake ofdescription only, as ‘east’ relative to the ‘north’ previouslydescribed. In a second illumination mode of FIG. 2E, aperture plate 13Wis used to provide similar illumination, but from an opposite direction,labeled ‘west’. FIG. 2E illustrates two further types of off-axisillumination mode. In a first illumination mode of FIG. 2E, apertureplate 13NW provides off-axis illumination from the directions designated‘north’ and ‘west’ as previously described. In a second illuminationmode, aperture plate 13SE is used to provide similar illumination, butfrom an opposite direction, labeled ‘south’ and ‘east’ as previouslydescribed. The use of these, and numerous other variations andapplications of the apparatus are described in, for example, the priorpublished patent application publications mentioned above.

FIG. 2F depicts an example composite metrology target formed on asubstrate. The composite target comprises four periodic structures (inthis case, gratings) 32, 33, 34, 35 positioned closely together. In anembodiment, the periodic structures are positioned closely togetherenough so that they all are within a measurement spot 31 formed by theillumination beam of the metrology apparatus. In that case, the fourperiodic structures thus are all simultaneously illuminated andsimultaneously imaged on sensors 19 and 23. In an example dedicated tooverlay measurement, periodic structures 32, 33, 34, 35 are themselvescomposite periodic structures (e.g., composite gratings) formed byoverlying periodic structures, i.e., periodic structures are patternedin different layers of the device formed on substrate W and such that atleast one periodic structure in one layer overlays at least one periodicstructure in a different layer. Such a target may have outer dimensionswithin 20 μm×20 μm or within 16 μm×16 μm. Further, all the periodicstructures are used to measure overlay between a particular pair oflayers. To facilitate a target being able to measure more than a singlepair of layers, periodic structures 32, 33, 34, 35 may have differentlybiased overlay offsets in order to facilitate measurement of overlaybetween different layers in which the different parts of the compositeperiodic structures are formed. Thus, all the periodic structures forthe target on the substrate would be used to measure one pair of layersand all the periodic structures for another same target on the substratewould be used to measure another pair of layers, wherein the differentbias facilitates distinguishing between the layer pairs.

FIG. 2G shows an example of an image that may be formed on and detectedby the sensor 23, using the target of FIG. 2F in the apparatus of FIG.2B, using the aperture plates 13NW or 13SE from FIG. 2E. While thesensor 19 cannot resolve the different individual periodic structures 32to 35, the sensor 23 can do so. The dark rectangle represents the fieldof the image on the sensor, within which the illuminated spot 31 on thesubstrate is imaged into a corresponding circular area 41. Within this,rectangular areas 42-45 represent the images of the periodic structures32 to 35. If the periodic structures are located in product areas,product features may also be visible in the periphery of this imagefield. Image processor and controller PU processes these images usingpattern recognition to identify the separate images 42 to 45 of periodicstructures 32 to 35. In this way, the images do not have to be alignedvery precisely at a specific location within the sensor frame, whichgreatly improves throughput of the measuring apparatus as a whole.

In the context of a semiconductor device fabrication process, todetermine whether a substrate measurement recipe is accurate and toobtain the true value from the measurement results may be challengingbecause the true value and the systematic errors both manifest in theresults of the measurement. Namely, they both affect the results andthus the results can have contribution from the true value andcontribution from the systematic errors. If the contribution of thesystematic errors can be determined, the true value may be determinedfrom the results of the measurement, subject to random errors (i.e.,imprecision). The random errors (i.e., imprecision) of a measurement maybe attributed the nature of the measurement, the apparatus used for themeasurement, the environment, or even the physics involved in themeasurement. Random errors or imprecision can be reduced by repeatedmeasurements because random errors in repeated measurements average tozero. FIG. 4A and FIG. 4B demonstrate how the same target may introducedifferent systematic errors in different substrate measurement recipes.FIG. 4A schematically shows a cross-sectional view of a target 310including an upper structure 311 over a trench 312, suitable formeasuring overlay error between the upper structure 311 and the trench312. The bottom 313 of the trench 312 is tilted (not parallel to thesubstrate) because of the process (e.g., etch, CMP, or other steps inthe process). For example, two otherwise identical substrate measurementrecipes use light beams 314 and 315 at the same incidence angle forsubstrate measurement, except that the light beams 314 and 315 aredirected from different directions onto the substrate. Although thebeams 314 and 315 have the same angle of incidence relative to thesubstrate, they do not have the same angle of incidence relative to thebottom 313 of the trench 312 because the bottom 313 is tilted relativeto the substrate. Therefore, characteristics of the scattering of thebeams 314 and 315 by the target are different.

FIG. 4B schematically shows a cross-sectional view of another target 320including an upper structure 321 over a trench 322, suitable formeasuring overlay error between the upper structure 321 and the trench322. The sidewall 323 of the trench 322 is tilted (not perpendicular tothe substrate) because of the process (e.g., etch, CMP, or other stepsin the process). For example, two otherwise identical substratemeasurement recipes use light beams 324 and 325 at the same incidenceangle for substrate measurement, except that the light beams 324 and 325are directed from different directions onto the substrate. Although thebeams 324 and 325 have the same angle of incidence relative to thesubstrate, the beam 324 glances off the sidewall 323 while the beam 325is almost normal to the sidewall 323. The beam 324 thus is barelyscattered by the sidewall 323 but the beam 325 is strongly scattered bythe sidewall 323. Therefore, characteristics of the scattering of thebeams 324 and 325 by the target are different.

One way to determine the contribution of the systematic errors ismodeling. If the cause of the systematic errors can be measured and therelationship between the cause to the contribution of the systematicerrors is known, the contribution of the systematic errors can bedetermined from the measured cause and the relationship.

FIG. 5A shows two diffraction images I_(R) and I_(L)·I_(R) is themeasurement result using a substrate measurement recipe with anintensity distribution 510 at the pupil plane that has a uniformnon-zero value on the left half and is zero on the right half; I_(L) isthe measurement result using a substrate measurement recipe with anintensity distribution 520 at the pupil plane that has a uniformnon-zero value on the right half and is zero on the left half. FIG. 5Bshows the pattern from which the two diffraction images are obtained.The average difference between the two diffraction images I_(R) andI_(L) may be used to derive by modeling the systematic error caused byasymmetry of the pattern (e.g., tilted bottom, tilted sidewall), becausethe average difference and the asymmetry has a definite relationship.FIG. 5C, FIG. 5D and FIG. 5E each show the average difference (verticalaxes) between the two diffraction images I_(R) and I_(L) as a functionof position (horizontal axes), respectively with zero to increasingamounts of asymmetry. FIG. 5C, FIG. 5D and FIG. 5E indicate that higherasymmetry leads to higher average difference between the two diffractionimages. The average difference between the two diffraction images I_(R)and I_(L) may be in a form of (I_(L)−I_(R))/(I_(L)+I_(R)).

Another way to determine the contribution of the systematic errors andthe true value is to reconstruct the pattern measured. Reconstruction asused herein means determination of a three-dimensional ortwo-dimensional structure of the pattern measured. Once the structure ofthe pattern is known, the systematic errors can simply be determinedfrom that structure. For example, if the structure of the target 310 isknown, the true value of the position of the upper structure 311relative to the trench 312 can simply be determined geometrically fromthe structure of the target 310.

Reconstruction may use measurement results obtained using multipledifferent substrate measurement recipes. For example, the pattern may bemeasured using substrate measurement recipes with different intensitydistributions at the pupil plane of the metrology tool.

FIG. 6 schematically shows a flow for reconstruction. A pattern 610 ismeasured using multiple different substrate measurement recipes 620-1,620-2, . . . , 620-n. Measurement results 630-1, 630-2, . . . , 630-nare obtained using these substrate measurement recipes, respectively.The measurement results 630-1, 630-2, . . . , 630-n are used as input toa reconstruction algorithm 640. The reconstruction algorithm 640 outputsthe structure 650 of the pattern 610. The reconstruction algorithm 640used may depend on the nature of the substrate measurement recipes620-1, 620-2, . . . , 620-n. Examples of reconstruction algorithmsinclude the Algebraic Reconstruction Technique (ART) and the Radontransform (including inverse Radon transform). The AlgebraicReconstruction Technique is a class of iterative algorithms used incomputed tomography, and reconstruct an image from a series of angularprojections (a sinogram). The Radon transform is the integral transformincludes the integral of a function along a path l. The Radon transformof an image f({right arrow over (r)}) is R(l)[f({right arrow over(r)})]=∫_(l)f({right arrow over (r)})d{right arrow over (r)}. The path lmay be a straight line or a curve. Other examples of reconstructionalgorithms include the projection-slice theorem. The projection-slicetheorem states that the Fourier transform of the projection of anN-dimensional function f({right arrow over (r)}) onto an m-dimensionallinear submanifold is equal to an m-dimensional slice of theN-dimensional Fourier transform of that function consisting of anm-dimensional linear submanifold through the origin in the Fourier spacewhich is parallel to the projection submanifold.

The reconstruction algorithm 640 may not have to use the entirety ofeach of measurement results 630-1, 630-2, . . . , 630-n. For example,FIGS. 7A-7D each show a different intensity distribution at the pupilplane, the image it leads to, and the portion of the image used by thereconstruction algorithm 640. In this example, only a quarter of theeach image is used.

FIG. 8 schematically shows an example of reconstruction of a pattern810. A series of images 830 are obtained from the pattern 810 usingsubstrate measurement recipes with a series of different intensitydistributions 820 at the pupil plane. The images 830 are used to derivea reconstructed pattern 840 that is similar to the pattern 810.

FIGS. 9A-9C schematically show several uses of the reconstructedpattern. In FIG. 9A, the pattern includes at least two sub-patterns onthe same layer. The location of an edge of a sub-pattern relative toanother sub-pattern may be determined from the reconstructed pattern.The location of the edge can be used to determine edge placement error(EPE). The location of the edge may also be used to align the patterningdevice to the pattern. In FIG. 9B, a dimension of the pattern may bedetermined from the reconstructed pattern. The dimension may be acritical dimension (CD). In FIG. 9C, the pattern includes at least twosub-patterns on different layers. The location of a sub-pattern relativeto the other sub-pattern may be determined from the reconstructedpattern. This location may be used to determined alignment between thedifferent layers.

FIG. 10 is a block diagram that illustrates a computer system 100 whichcan assist in implementing the methods and flows disclosed herein.Computer system 100 includes a bus 102 or other communication mechanismto communicate information, and a processor 104 (or multiple processors104 and 105) coupled with bus 102 to process information. Computersystem 100 may also include a main memory 106, such as a random accessmemory (RAM) or other dynamic storage device, coupled to bus 102 tostore and/or supply information and instructions to be executed byprocessor 104. Main memory 106 may be used to store and/or supplytemporary variables or other intermediate information during executionof instructions to be executed by processor 104. Computer system 100 mayfurther include a read only memory (ROM) 108 or other static storagedevice coupled to bus 102 to store and/or supply static information andinstructions for processor 104. A storage device 110, such as a magneticdisk or optical disk, may be provided and coupled to bus 102 to storeand/or supply information and instructions.

Computer system 100 may be coupled via bus 102 to a display 112, such asa cathode ray tube (CRT) or flat panel or touch panel display, todisplay information to a computer user. An input device 114, includingalphanumeric and other keys, may be coupled to bus 102 to communicateinformation and command selections to processor 104. Another type ofuser input device may be cursor control 116, such as a mouse, atrackball, or cursor direction keys, to communicate directioninformation and command selections to processor 104 and to controlcursor movement on display 112. This input device typically has twodegrees of freedom in two axes, a first axis (e.g., x) and a second axis(e.g., y), that allows the device to specify positions in a plane. Atouch panel (screen) display may also be used as an input device.

According to one embodiment, portions of the optimization process may beperformed by computer system 100 in response to processor 104 executingone or more sequences of one or more instructions contained in mainmemory 106. Such instructions may be read into main memory 106 fromanother computer-readable medium, such as storage device 110. Executionof the sequences of instructions contained in main memory 106 causesprocessor 104 to perform the process steps described herein. One or moreprocessors in a multi-processing arrangement may be employed to executethe sequences of instructions contained in main memory 106. In analternative embodiment, hard-wired circuitry may be used in place of orin combination with software instructions. Thus, the description hereinis not limited to any specific combination of hardware circuitry andsoftware.

The term “computer-readable medium” as used herein refers to any mediumthat participates in providing instructions to processor 104 forexecution. Such a medium may take many forms, including but not limitedto, non-volatile media, volatile media, and transmission media.Non-volatile media include, for example, optical or magnetic disks, suchas storage device 110. Volatile media include dynamic memory, such asmain memory 106. Transmission media include coaxial cables, copper wireand fiber optics, including the wires that comprise bus 102.Transmission media can also take the form of acoustic or light waves,such as those generated during radio frequency (RF) and infrared (IR)data communications. Common forms of computer-readable media include,for example, a floppy disk, a flexible disk, hard disk, magnetic tape,any other magnetic medium, a CD-ROM, DVD, any other optical medium,punch cards, paper tape, any other physical medium with patterns ofholes, a RAM, a PROM, and EPROM, a FLASH-EPROM, any other memory chip orcartridge, a carrier wave as described hereinafter, or any other mediumfrom which a computer can read.

Various forms of computer readable media may be involved in carrying oneor more sequences of one or more instructions to processor 104 forexecution. For example, the instructions may initially be borne on adisk or memory of a remote computer. The remote computer can load theinstructions into its dynamic memory and send the instructions over acommunications path. Computer system 100 can receive the data from thepath and place the data on bus 102. Bus 102 carries the data to mainmemory 106, from which processor 104 retrieves and executes theinstructions. The instructions received by main memory 106 mayoptionally be stored on storage device 110 either before or afterexecution by processor 104.

Computer system 100 may include a communication interface 118 coupled tobus 102. Communication interface 118 provides a two-way datacommunication coupling to a network link 120 that is connected to anetwork 122. For example, communication interface 118 may provide awired or wireless data communication connection. In any suchimplementation, communication interface 118 sends and receiveselectrical, electromagnetic or optical signals that carry digital datastreams representing various types of information.

Network link 120 typically provides data communication through one ormore networks to other data devices. For example, network link 120 mayprovide a connection through network 122 to a host computer 124 or todata equipment operated by an Internet Service Provider (ISP) 126. ISP126 in turn provides data communication services through the worldwidepacket data communication network, now commonly referred to as the“Internet” 128. Network 122 and Internet 128 both use electrical,electromagnetic or optical signals that carry digital data streams. Thesignals through the various networks and the signals on network link 120and through communication interface 118, which carry the digital data toand from computer system 100, are exemplary forms of carrier wavestransporting the information.

Computer system 100 can send messages and receive data, includingprogram code, through the network(s), network link 120, andcommunication interface 118. In the Internet example, a server 130 mighttransmit a requested code for an application program through Internet128, ISP 126, network 122 and communication interface 118. One suchdownloaded application may provide for the code to implement a methodherein, for example. The received code may be executed by processor 104as it is received, and/or stored in storage device 110, or othernon-volatile storage for later execution. In this manner, computersystem 100 may obtain application code in the form of a carrier wave.

FIG. 11 schematically depicts an exemplary lithographic apparatus. Theapparatus comprises:

an illumination system IL, to condition a beam B of radiation. In thisparticular case, the illumination system also comprises a radiationsource SO;

a first object table (e.g., mask table) MT provided with a patterningdevice holder to hold a patterning device MA (e.g., a reticle), andconnected to a first positioner PM to accurately position the patterningdevice with respect to item PS;

a second object table (substrate table) WT provided with a substrateholder to hold a substrate W (e.g., a resist-coated silicon wafer), andconnected to a second positioner PW to accurately position the substratewith respect to item PS;

a projection system PS (e.g., a refractive, catoptric or catadioptricoptical system) to image an irradiated portion of the patterning deviceMA onto a target portion C (e.g., comprising one or more dies) of thesubstrate W.

As depicted herein, the apparatus is of a transmissive type (i.e., has atransmissive mask). However, in general, it may also be of a reflectivetype, for example (with a reflective mask). Alternatively, the apparatusmay employ another kind of patterning device as an alternative to theuse of a classic mask; examples include a programmable mirror array orLCD matrix.

The source SO (e.g., a mercury lamp or excimer laser) produces a beam ofradiation. This beam is fed into an illumination system (illuminator)IL, either directly or after having traversed a conditioner, such as abeam expander. The illuminator IL may comprise an adjuster AD configuredto set the outer and/or inner radial extent (commonly referred to asσ-outer and σ-inner, respectively) of the intensity distribution in thebeam. In addition, it will generally comprise various other components,such as an integrator IN and a condenser CO. In this way, the beam Bimpinging on the patterning device MA has a desired uniformity andintensity distribution in its cross-section.

It should be noted with regard to FIG. 11 that the source SO may bewithin the housing of the lithographic apparatus (as is often the casewhen the source SO is a mercury lamp, for example), but that it may alsobe remote from the lithographic apparatus, the radiation beam that itproduces being led into the apparatus (e.g., with the aid of suitabledirecting mirrors BD); this latter scenario is often the case when thesource SO is an excimer laser (e.g., based on KrF, ArF or F₂ lasing).

The beam B subsequently intercepts the patterning device MA, which isheld on a patterning device table MT. Having traversed the patterningdevice MA, the beam B passes through the projection system PS, whichfocuses the beam B onto a target portion C of the substrate W. With theaid of the second positioner PW (and interferometer IF), the substratetable WT can be moved accurately, e.g. so as to position differenttarget portions C in the path of the beam B. Similarly, the firstpositioner PM can be used to accurately position the patterning deviceMA with respect to the path of the beam B, e.g., after mechanicalretrieval of the patterning device MA from a patterning device library,or during a scan. In general, movement of the object tables MT, WT willbe realized with the aid of a long-stroke module (coarse positioning)and a short-stroke module (fine positioning), which are not explicitlydepicted in FIG. 11.

Patterning device (e.g., mask) MA and substrate W may be aligned usingmask alignment marks M1, M2 and substrate alignment marks P1, P2.Although the substrate alignment marks as illustrated occupy dedicatedtarget portions, they may be located in spaces between target portions(these are known as scribe-lane alignment marks). Similarly, insituations in which more than one die is provided on the patterningdevice (e.g., mask) MA, the patterning device alignment marks may belocated between the dies. Small alignment markers may also be includedwithin dies, in amongst the device features, in which case it isdesirable that the markers be as small as possible and not require anydifferent imaging or process conditions than adjacent features.

FIG. 12 schematically depicts another exemplary lithographic apparatus1000. The lithographic apparatus 1000 includes:

a source collector module SO

an illumination system (illuminator) IL configured to condition aradiation beam B (e.g. EUV radiation).

a support structure (e.g. a mask table) MT constructed to support apatterning device (e.g. a mask or a reticle) MA and connected to a firstpositioner PM configured to accurately position the patterning device;

a substrate table (e.g. a wafer table) WT constructed to hold asubstrate (e.g. a resist coated wafer) W and connected to a secondpositioner PW configured to accurately position the substrate; and

a projection system (e.g. a reflective projection system) PS configuredto project a pattern imparted to the radiation beam B by patterningdevice MA onto a target portion C (e.g. comprising one or more dies) ofthe substrate W.

As here depicted, the apparatus 1000 is of a reflective type (e.g.employing a reflective mask). It is to be noted that because mostmaterials are absorptive within the EUV wavelength range, the patterningdevice may have a multilayer reflector comprising, for example, amulti-stack of molybdenum and silicon. In one example, the multi-stackreflector has a 40 layer pairs of molybdenum and silicon. Even smallerwavelengths may be produced with X-ray lithography. Since most materialis absorptive at EUV and x-ray wavelengths, a thin piece of patternedabsorbing material on the patterning device topography (e.g., a TaNabsorber on top of the multi-layer reflector) defines where featureswould print (positive resist) or not print (negative resist).

Referring to FIG. 12, the illuminator IL receives an extreme ultraviolet (EUV) radiation beam from the source collector module SO. Methodsto produce EUV radiation include, but are not necessarily limited to,converting a material into a plasma state that has at least one element,e.g., xenon, lithium or tin, with one or more emission lines in the EUVrange. In one such method, often termed laser produced plasma (“LPP”)the plasma can be produced by irradiating a fuel, such as a droplet,stream or cluster of material having the line-emitting element, with alaser beam. The source collector module SO may be part of an EUVradiation system including a laser, not shown in FIG. 12, to provide thelaser beam to excite the fuel. The resulting plasma emits outputradiation, e.g., EUV radiation, which is collected using a radiationcollector, disposed in the source collector module. The laser and thesource collector module may be separate entities, for example when a CO₂laser is used to provide the laser beam for fuel excitation.

In such cases, the laser is not considered to form part of thelithographic apparatus and the radiation beam is passed from the laserto the source collector module with the aid of a beam delivery systemcomprising, for example, suitable directing mirrors and/or a beamexpander. In other cases the source may be an integral part of thesource collector module, for example when the source is a dischargeproduced plasma EUV generator, often termed as a DPP source.

The illuminator IL may comprise an adjuster configured to adjust theangular intensity distribution of the radiation beam. Generally, atleast the outer and/or inner radial extent (commonly referred to asσ-outer and σ-inner, respectively) of the intensity distribution in apupil plane of the illuminator can be adjusted. In addition, theilluminator IL may comprise various other components, such as facettedfield and pupil mirror devices. The illuminator may be used to conditionthe radiation beam, to have a desired uniformity and intensitydistribution in its cross section.

The radiation beam B is incident on the patterning device (e.g., mask)MA, which is held on the support structure (e.g., mask table) MT, and ispatterned by the patterning device. After being reflected from thepatterning device (e.g. mask) MA, the radiation beam B passes throughthe projection system PS, which focuses the beam onto a target portion Cof the substrate W. With the aid of the second positioner PW andposition sensor PS2 (e.g. an interferometric device, linear encoder orcapacitive sensor), the substrate table WT can be moved accurately, e.g.so as to position different target portions C in the path of theradiation beam B. Similarly, the first positioner PM and anotherposition sensor PS1 can be used to accurately position the patterningdevice (e.g. mask) MA with respect to the path of the radiation beam B.Patterning device (e.g. mask) MA and substrate W may be aligned usingpatterning device alignment marks M1, M2 and substrate alignment marksP1, P2.

The depicted apparatus could be used in at least one of the followingmodes:

1. In step mode, the support structure (e.g. mask table) MT and thesubstrate table WT are kept essentially stationary, while an entirepattern imparted to the radiation beam is projected onto a targetportion C at one time (i.e. a single static exposure). The substratetable WT is then shifted in the X and/or Y direction so that a differenttarget portion C can be exposed.

2. In scan mode, the support structure (e.g. mask table) MT and thesubstrate table WT are scanned synchronously in a given direction (theso-called “scan direction”) while a pattern imparted to the radiationbeam is projected onto a target portion C (i.e. a single dynamicexposure). The velocity and direction of the substrate table WT relativeto the support structure (e.g. mask table) MT may be determined by the(de-)magnification and image reversal characteristics of the projectionsystem PS.

3. In another mode, the support structure (e.g. mask table) MT is keptessentially stationary holding a programmable patterning device, and thesubstrate table WT is moved or scanned while a pattern imparted to theradiation beam is projected onto a target portion C. In this mode,generally a pulsed radiation source is employed and the programmablepatterning device is updated as required after each movement of thesubstrate table WT or in between successive radiation pulses during ascan. This mode of operation can be readily applied to masklesslithography that utilizes programmable patterning device, such as aprogrammable mirror array of a type as referred to above.

Further, the lithographic apparatus may be of a type having two or moretables (e.g., two or more substrate table, two or more patterning devicetables, and/or a substrate table and a table without a substrate). Insuch “multiple stage” devices the additional tables may be used inparallel, or preparatory steps may be carried out on one or more tableswhile one or more other tables are being used for exposures. Twin stagelithographic apparatuses are described, for example, in U.S. Pat. No.5,969,441, incorporated herein by reference in its entirety.

FIG. 13 shows the apparatus 1000 in more detail, including the sourcecollector module SO, the illumination system IL, and the projectionsystem PS. The source collector module SO is constructed and arrangedsuch that a vacuum environment can be maintained in an enclosingstructure 220 of the source collector module SO. An EUV radiationemitting plasma 210 may be formed by a discharge produced plasma source.EUV radiation may be produced by a gas or vapor, for example Xe gas, Livapor or Sn vapor in which the very hot plasma 210 is created to emitradiation in the EUV range of the electromagnetic spectrum. The very hotplasma 210 is created by, for example, an electrical discharge causingan at least partially ionized plasma. Partial pressures of, for example,10 Pa of Xe, Li, Sn vapor or any other suitable gas or vapor may berequired for efficient generation of the radiation. In an embodiment, aplasma of excited tin (Sn) is provided to produce EUV radiation.

The radiation emitted by the hot plasma 210 is passed from a sourcechamber 211 into a collector chamber 212 via an optional gas barrier orcontaminant trap 230 (in some cases also referred to as contaminantbarrier or foil trap) which is positioned in or behind an opening insource chamber 211. The contaminant trap 230 may include a channelstructure. Contamination trap 230 may also include a gas barrier or acombination of a gas barrier and a channel structure. The contaminanttrap or contaminant barrier 230 further indicated herein at leastincludes a channel structure, as known in the art.

The collector chamber 211 may include a radiation collector CO which maybe a so-called grazing incidence collector. Radiation collector CO hasan upstream radiation collector side 251 and a downstream radiationcollector side 252. Radiation that traverses collector CO can bereflected off a grating spectral filter 240 to be focused in a virtualsource point IF along the optical axis indicated by the dot-dashed line‘O’. The virtual source point IF is commonly referred to as theintermediate focus, and the source collector module is arranged suchthat the intermediate focus IF is located at or near an opening 221 inthe enclosing structure 220. The virtual source point IF is an image ofthe radiation emitting plasma 210.

Subsequently the radiation traverses the illumination system IL, whichmay include a facetted field mirror device 22 and a facetted pupilmirror device 24 arranged to provide a desired angular distribution ofthe radiation beam 21, at the patterning device MA, as well as a desireduniformity of radiation intensity at the patterning device MA. Uponreflection of the beam of radiation 21 at the patterning device MA, heldby the support structure MT, a patterned beam 26 is formed and thepatterned beam 26 is imaged by the projection system PS via reflectiveelements 28, 30 onto a substrate W held by the substrate table WT.

More elements than shown may generally be present in illumination opticsunit IL and projection system PS. The grating spectral filter 240 mayoptionally be present, depending upon the type of lithographicapparatus. Further, there may be more mirrors present than those shownin the figures, for example there may be 1-6 additional reflectiveelements present in the projection system PS than shown in FIG. 13.

Collector optic CO, as illustrated in FIG. 13, is depicted as a nestedcollector with grazing incidence reflectors 253, 254 and 255, just as anexample of a collector (or collector mirror). The grazing incidencereflectors 253, 254 and 255 are disposed axially symmetric around theoptical axis O and a collector optic CO of this type is desirably usedin combination with a discharge produced plasma source, often called aDPP source. Alternatively, the source collector module SO may be part ofan LPP radiation system.

The term “projection system” used herein should be broadly interpretedas encompassing any type of projection system, including refractive,reflective, catadioptric, magnetic, electromagnetic and electrostaticoptical systems, or any combination thereof, as appropriate for theexposure radiation being used, or for other factors such as the use ofan immersion liquid or the use of a vacuum.

The lithographic apparatus may also be of a type wherein at least aportion of the substrate may be covered by a liquid having a relativelyhigh refractive index, e.g., water, so as to fill a space between theprojection system and the substrate. An immersion liquid may also beapplied to other spaces in the lithographic apparatus, for example,between the mask and the projection system. Immersion techniques arewell known in the art for increasing the numerical aperture ofprojection systems. The term “immersion” as used herein does not meanthat a structure, such as a substrate, must be submerged in liquid, butrather only means that liquid is located between the projection systemand the substrate during exposure.

The concepts disclosed herein may be used to simulate or mathematicallymodel any device manufacturing process involving a lithographicapparatus, and may be especially useful with emerging imagingtechnologies capable of producing wavelengths of an increasingly smallersize. Emerging technologies already in use include deep ultraviolet(DUV) lithography that is capable of producing a 193 nm wavelength withthe use of an ArF laser, and even a 157 nm wavelength with the use of afluorine laser. Moreover, EUV lithography is capable of producingwavelengths within a range of 5-20 nm.

While the concepts disclosed herein may be used for device manufacturingon a substrate such as a silicon wafer, it shall be understood that thedisclosed concepts may be used with any type of lithographic imagingsystems, e.g., those used for imaging on substrates other than siliconwafers.

The patterning device referred to above comprises or can form a designlayout. The design layout can be generated utilizing a CAD(computer-aided design) program. This process is often referred to asEDA (electronic design automation). Most CAD programs follow a set ofpredetermined design rules in order to create functional designlayouts/patterning devices. These rules are set by processing and designlimitations. For example, design rules define the space tolerancebetween circuit devices (such as gates, capacitors, etc.) orinterconnect lines, so as to ensure that the circuit devices or lines donot interact with one another in an undesirable way. The design rulelimitations are typically referred to as “critical dimensions” (CD). Acritical dimension of a circuit can be defined as the smallest width ofa line or hole or the smallest space between two lines or two holes.Thus, the CD determines the overall size and density of the designedcircuit. Of course, one of the goals in integrated circuit fabricationis to faithfully reproduce the original circuit design on the substrate(via the patterning device).

The term “mask” or “patterning device” as employed in this text may bebroadly interpreted as referring to a generic patterning device that canbe used to endow an incoming radiation beam with a patternedcross-section, corresponding to a pattern that is to be created in atarget portion of the substrate; the term “light valve” can also be usedin this context. Besides the classic mask (transmissive or reflective;binary, phase-shifting, hybrid, etc.), examples of other such patterningdevices include:

a programmable mirror array. An example of such a device is amatrix-addressable surface having a viscoelastic control layer and areflective surface. The basic principle behind such an apparatus is that(for example) addressed areas of the reflective surface reflect incidentradiation as diffracted radiation, whereas unaddressed areas reflectincident radiation as undiffracted radiation. Using an appropriatefilter, the said undiffracted radiation can be filtered out of thereflected beam, leaving only the diffracted radiation behind; in thismanner, the beam becomes patterned according to the addressing patternof the matrix-addressable surface. The required matrix addressing can beperformed using suitable electronic means. More information on suchmirror arrays can be gleaned, for example, from U.S. Pat. Nos. 5,296,891and 5,523,193, which are incorporated herein by reference.

a programmable LCD array. An example of such a construction is given inU.S. Pat. No. 5,229,872, which is incorporated herein by reference.

As noted, microlithography is a significant step in the manufacturing ofdevices such as ICs, where patterns formed on substrates definefunctional elements of the ICs, such as microprocessors, memory chipsetc. Similar lithographic techniques are also used in the formation offlat panel displays, micro-electro mechanical systems (MEMS) and otherdevices.

The process in which features with dimensions smaller than the classicalresolution limit of a lithographic apparatus are printed, is commonlyknown as low-k₁ lithography, according to the resolution formulaCD=k₁×λ/NA, where λ is the wavelength of radiation employed (currentlyin most cases 248 nm or 193 nm), NA is the numerical aperture ofprojection optics in the lithographic apparatus, CD is the “criticaldimension”—generally the smallest feature size printed—and k₁ is anempirical resolution factor. In general, the smaller k₁ the moredifficult it becomes to reproduce a pattern on the substrate thatresembles the shape and dimensions planned by a circuit designer inorder to achieve particular electrical functionality and performance. Toovercome these difficulties, sophisticated fine-tuning steps are appliedto the lithographic apparatus and/or design layout. These include, forexample, but not limited to, optimization of NA and optical coherencesettings, customized illumination schemes, use of phase shiftingpatterning devices, optical proximity correction (OPC, sometimes alsoreferred to as “optical and process correction”) in the design layout,or other methods generally defined as “resolution enhancementtechniques” (RET).

As an example, OPC addresses the fact that the final size and placementof an image of the design layout projected on the substrate will not beidentical to, or simply depend only on the size and placement of thedesign layout on the patterning device. A person skilled in the art willrecognize that, especially in the context of lithographysimulation/optimization, the term “mask”/“patterning device” and “designlayout” can be used interchangeably, as in lithographysimulation/optimization, a physical patterning device is not necessarilyused but a design layout can be used to represent a physical patterningdevice. For the small feature sizes and high feature densities presenton some design layout, the position of a particular edge of a givenfeature will be influenced to a certain extent by the presence orabsence of other adjacent features. These proximity effects arise fromminute amounts of radiation coupled from one feature to another and/ornon-geometrical optical effects such as diffraction and interference.Similarly, proximity effects may arise from diffusion and other chemicaleffects during post-exposure bake (PEB), resist development, and etchingthat generally follow lithography.

To help ensure that the projected image of the design layout is inaccordance with requirements of a given target circuit design, proximityeffects may be predicted and compensated for, using sophisticatednumerical models, corrections or pre-distortions of the design layout.The article “Full-Chip Lithography Simulation and Design Analysis—HowOPC Is Changing IC Design”, C. Spence, Proc. SPIE, Vol. 5751, pp 1-14(2005) provides an overview of current “model-based” optical proximitycorrection processes. In a typical high-end design almost every featureof the design layout has some modification in order to achieve highfidelity of the projected image to the target design. Thesemodifications may include shifting or biasing of edge positions or linewidths as well as application of “assist” features that are intended toassist projection of other features.

Applying OPC is generally not an “exact science”, but an empirical,iterative process that does not always compensate for all possibleproximity effect. Therefore, the effect of OPC, e.g., design layoutsafter application of OPC and any other RET, should be verified by designinspection, i.e. intensive full-chip simulation using calibratednumerical process models, in order to minimize the possibility of designflaws being built into the patterning device pattern.

Both OPC and full-chip RET verification may be based on numericalmodeling systems and methods as described, for example in, U.S. PatentApplication Publication No. US 2005-0076322 and an article titled“Optimized Hardware and Software For Fast, Full Chip Simulation”, by Y.Cao et al., Proc. SPIE, Vol. 5754, 405 (2005).

One RET is related to adjustment of the global bias of the designlayout. The global bias is the difference between the patterns in thedesign layout and the patterns intended to print on the substrate. Forexample, a circular pattern of 25 nm diameter may be printed on thesubstrate by a 50 nm diameter pattern in the design layout or by a 20 nmdiameter pattern in the design layout but with high dose.

In addition to optimization to design layouts or patterning devices(e.g., OPC), the illumination source can also be optimized, eitherjointly with patterning device optimization or separately, in an effortto improve the overall lithography fidelity. The terms “illuminationsource” and “source” are used interchangeably in this document. As isknown, off-axis illumination, such as annular, quadrupole, and dipole,is a proven way to resolve fine structures (i.e., target features)contained in the patterning device. However, when compared to atraditional illumination source, an off-axis illumination source usuallyprovides less radiation intensity for the aerial image (AI). Thus, itbecomes desirable to attempt to optimize the illumination source toachieve the optimal balance between finer resolution and reducedradiation intensity.

Numerous illumination source optimization approaches can be found, forexample, in an article by Rosenbluth et al., titled “Optimum Mask andSource Patterns to Print A Given Shape”, Journal of Microlithography,Microfabrication, Microsystems 1(1), pp. 13-20, (2002). The source ispartitioned into several regions, each of which corresponds to a certainregion of the pupil spectrum. Then, the source distribution is assumedto be uniform in each source region and the brightness of each region isoptimized for the process window. In another example set forth in anarticle by Granik, titled “Source Optimization for Image Fidelity andThroughput”, Journal of Microlithography, Microfabrication, Microsystems3(4), pp. 509-522, (2004), several existing source optimizationapproaches are overviewed and a method based on illuminator pixels isproposed that converts the source optimization problem into a series ofnon-negative least square optimizations.

For low k₁ photolithography, optimization of both the source andpatterning device is useful to ensure a viable process window forprojection of critical circuit patterns. Some algorithms discretizeillumination into independent source points and the patterning devicepattern into diffraction orders in the spatial frequency domain, andseparately formulate a cost function (which is defined as a function ofselected design variables) based on process window metrics such asexposure latitude which could be predicted by optical imaging modelsfrom source point intensities and patterning device diffraction orders.The term “design variables” as used herein comprises a set of parametersof an apparatus or a device manufacturing process, for example,parameters a user of the lithographic apparatus can adjust, or imagecharacteristics a user can adjust by adjusting those parameters. Itshould be appreciated that any characteristics of a device manufacturingprocess, including those of the source, the patterning device, theprojection optics, and/or resist characteristics can be among the designvariables in the optimization. The cost function is often a non-linearfunction of the design variables. Then standard optimization techniquesare used to minimize the cost function.

A source and patterning device (design layout) optimization method andsystem that allows for simultaneous optimization of the source andpatterning device using a cost function without constraints and within apracticable amount of time is described in a commonly assigned PCTPatent Application Publication No. WO2010/059954, which is herebyincorporated by reference in its entirety.

Another source and mask optimization method and system that involvesoptimizing the source by adjusting pixels of the source is described inU.S. Patent Application Publication No. 2010/0315614, which is herebyincorporated by reference in its entirety.

The term “projection optics” as used herein should be broadlyinterpreted as encompassing various types of optical systems, includingrefractive optics, reflective optics, apertures and catadioptric optics,for example. The term “projection optics” may also include componentsoperating according to any of these design types for directing, shapingor controlling the projection beam of radiation, collectively orsingularly. The term “projection optics” may include any opticalcomponent in the lithographic apparatus, no matter where the opticalcomponent is located on an optical path of the lithographic apparatus.Projection optics may include optical components for shaping, adjustingand/or projecting radiation from the source before the radiation passesthe patterning device, and/or optical components for shaping, adjustingand/or projecting the radiation after the radiation passes thepatterning device. The projection optics generally exclude the sourceand the patterning device.

The invention may further be described using the following clauses:

1. A method comprising:

obtaining a plurality of measurement results from a pattern on asubstrate respectively using a plurality of substrate measurementrecipes, the substrate processed by a lithography process;

reconstruct, using a computer, the pattern using the plurality ofmeasurement results, to obtain a reconstructed pattern.

2. The method of clause 1, wherein reconstructing the pattern is byusing the Algebraic Reconstruction Technique, the Radon transform, orthe projection-slice theorem.3. The method of any one of clauses 1 to 2, wherein reconstructing thepattern does not use the entirety of each of the plurality ofmeasurement results.4. The method of any one of clauses 1 to 3, wherein the plurality ofmeasurement results comprise diffraction images.5. The method of any one of clauses 1 to 4, wherein at least two of theplurality of substrate measurement recipes differ in intensitydistribution at a pupil plane of a metrology tool used in obtaining themeasurement results.6. The method of any one of clauses 1 to 5, wherein at least two of theplurality of substrate measurement recipes differ in a wavelength or apolarization of light used in obtaining the measurement results.7. The method of any one of clause 1 to 6, wherein the pattern has anasymmetry.8. The method of any one of clause 1 to 7, wherein the pattern has atilted bottom.9. The method of any one of clause 1 to 8, wherein the pattern has atilted sidewall.10. The method of any one of clause 1 to 9, wherein obtaining aplurality of measurement results comprises illuminating the pattern withultraviolet light or X-ray.11. The method of any one of clause 1 to 10, further comprisingdetermining an edge placement error or a dimension using thereconstructed pattern.12. The method of any one of clause 1 to 10, further comprising aligninga patterning device to the pattern using the reconstructed pattern.13. The method of any one of clause 1 to 10, further comprisingdetermining alignment between two sub-patterns of the pattern, whereinthe two sub-patterns are on different layers of the substrate.14. The method of any one of clause 1 to 10, further comprisingdetermining a true value of a measured characteristic of the pattern,using the reconstructed pattern.15. The method of any one of clauses 1 to 10, further comprisingdetermining a systematic error of a measured characteristic of thepattern, using the reconstructed pattern.16. A computer program product comprising a computer readable mediumhaving instructions recorded thereon, the instructions when executed bya computer implementing the method of any of clauses 1 to 15.

Although specific reference may have been made above to the use ofembodiments in the context of optical lithography, it will beappreciated that an embodiment of the invention may be used in otherapplications, for example imprint lithography, and where the contextallows, is not limited to optical lithography. In imprint lithography, atopography in a patterning device defines the pattern created on asubstrate. The topography of the patterning device may be pressed into alayer of resist supplied to the substrate whereupon the resist is curedby applying electromagnetic radiation, heat, pressure or a combinationthereof. The patterning device is moved out of the resist leaving apattern in it after the resist is cured. Thus, a lithographic apparatususing the imprint technology typically include a template holder to holdan imprint template, a substrate table to hold a substrate and one ormore actuators to cause relative movement between the substrate and theimprint template so that the pattern of the imprint template can beimprinted onto a layer of the substrate.

The descriptions above are intended to be illustrative, not limiting.Thus, it will be apparent to one skilled in the art that modificationsmay be made as described without departing from the scope of the claimsset out below.

1. A method comprising: obtaining a plurality of measurement resultsfrom a pattern on a substrate respectively using a plurality ofsubstrate measurement recipes performed by a metrology apparatus thatilluminates the pattern with radiation, the substrate processed by alithography process; and reconstruct, using a computer, the patternusing the plurality of measurement results, to obtain a reconstructedpattern.
 2. The method of claim 1, wherein reconstructing the pattern isby using a Algebraic Reconstruction Technique, Radon transform, orprojection-slice theorem.
 3. The method of claim 1, whereinreconstructing the pattern does not use a entirety of each of theplurality of measurement results.
 4. The method of claim 1, wherein theplurality of measurement results comprise diffraction images.
 5. Themethod of claims 1, wherein at least two of the plurality of substratemeasurement recipes differ in intensity distribution at a pupil plane ofa metrology tool used in obtaining the measurement results.
 6. Themethod of claim 1, wherein at least two of the plurality of substratemeasurement recipes differ in a wavelength or a polarization of lightused in obtaining the measurement results.
 7. The method of claim 1,wherein the pattern has at least one of an asymmetry, a tilted bottom,and a tilted sidewall.
 8. The method of claim 1, wherein obtaining aplurality of measurement results comprises illuminating the pattern withultraviolet light or X-ray.
 9. The method of claim 1, further comprisingdetermining an edge placement error or a dimension using thereconstructed pattern.
 10. The method of claim 1, further comprisingaligning a patterning device to the pattern using the reconstructedpattern.
 11. The method of claim 1, further comprising determiningalignment between two sub-patterns of the pattern, wherein the twosub-patterns are on different layers of the substrate.
 12. The method ofclaim 1, further comprising determining a true value of a measuredcharacteristic of the pattern, using the reconstructed pattern.
 13. Themethod of claim 1, further comprising determining a systematic error ofa measured characteristic of the pattern, using the reconstructedpattern.
 14. A computer program product comprising a computer readablemedium having instructions recorded thereon, the instructions whenexecuted by a computer implementing the method of claim 1.